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What is the x-intercept of the equation f(x) = -2cos(2 pi x)?

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What is the x-intercept of the equation f(x) = -2cos(2 pi x)?

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  1. 0 = -2cos(2pi(x))

    acos(0) = 2 pi (x)

    (+-) pi/2 , 3pi/2, 5pi/2, ...  = 2 pi (x)

    x =(+-) 1/4, 3/4, 5/4, ...


  2. f(x)== - 2 cos[ 2 TT x ]

    we have to resolve the trigonometric equation:

    - 2 Cos (2TT x) ==0 <===>

    Cos(2 TT x) == 0 <===> 2 TT x == TT/2+ k TT== (2k+1)/2 TT

    then x=={[ (2k+1)/2] TT }/ (2 TT) == (2K+1)/4  where k is a integer
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